IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v425y2022ics0096300322001187.html
   My bibliography  Save this article

Solving Fredholm integral equation of the first kind using Gaussian process regression

Author

Listed:
  • Qiu, Renjun
  • Yan, Liang
  • Duan, Xiaojun

Abstract

Fredholm integral equation of the first kind is a typical ill-posed problem, and it is usually difficult to obtain a stable numerical solution. In this paper, a new method is proposed to solve Fredholm integral equation using Gaussian process regression (GPR). The key to this method is that the right-hand term of the original integral equation is reconstructed by the GPR model to obtain a new integral equation in a reproducing kernel Hilbert spaces (RKHS). We present an analytical approximate solution of the new equation and prove that it converges to the exact minimal-norm solution of the original equation under the L2-norm. Especially, for the degenerate kernel equation, we obtain an explicit formula of the exact minimal-norm solution. Finally, the proposed method is verified to be very effective in solution accuracy by multiple examples.

Suggested Citation

  • Qiu, Renjun & Yan, Liang & Duan, Xiaojun, 2022. "Solving Fredholm integral equation of the first kind using Gaussian process regression," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    • Handle: RePEc:eee:apmaco:v:425:y:2022:i:c:s0096300322001187
    DOI: 10.1016/j.amc.2022.127032
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322001187
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127032?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Maleknejad, K. & Saeedipoor, E., 2017. "An efficient method based on hybrid functions for Fredholm integral equation of the first kind with convergence analysis," Applied Mathematics and Computation, Elsevier, vol. 304(C), pages 93-102.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      Corrections

      All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:425:y:2022:i:c:s0096300322001187. See general information about how to correct material in RePEc.

      If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

      If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

      For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

      Please note that corrections may take a couple of weeks to filter through the various RePEc services.

      IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.